f h(x) is the inverse of f(x), what is the value of h(f(x))

If \( h(x) \) is the inverse of \( f(x) \), then by the definition of inverse functions, applying \( h \) to \( f(x) \) returns the original input \( x \). In mathematical terms, this can be written as:

\[
h(f(x)) = x
\]

This is because the function \( f(x) \) maps \( x \) to some value, and the inverse function \( h(x) \) undoes that mapping, bringing it back to \( x \).

Would you like more details on inverse functions, or do you have any questions?

Here are 5 related questions to expand on this:

1. What is the formal definition of an inverse function?
2. How do you find the inverse of a function algebraically?
3. What is the graphical relationship between a function and its inverse?
4. Can all functions have inverses? Why or why not?
5. What happens if \( f(x) \) is not one-to-one? Can it still have an inverse?

**Tip**: A function must be one-to-one (injective) in order to have an inverse function.

If h(x) is the inverse of f(x), what is the value of h(f(x))?

Explore the solution to the problem of finding h(f(x)) when h(x) is the inverse of f(x). This involves key mathematical concepts such as inverse functions and function composition. Suitable for students in Grades 9-12, learn about the inverse function theorem and how it applies.

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